We'll prove that the category O of some class of Cherednik algebras is equivalent to a highest weight subcategory of the (parabolic) category O of affine gl_n. This implies, in particular, some conjectural Kazhdan-Lusztig type character formulas for the simple modules. The proof uses categorifications and highest weight theory. This is a joint work with R. Rouier, P. Shan and M. Varagnolo.